In order to mitigate the effect of nonlinear noise nonlinear Channel Equalizer (CE) based on Gaussian Processes for Regression (GPR) is proposed and experimentally demonstrated in an intensity modulation and direct detection fiber link. In this scheme, the GPR model is used to estimate the transmitted symbols or the corresponding nonlinear noise after pre-processing. The experimental results show that the nonlinear CE based on GPR has better performance than conventional linear and nonlinear filter-based CE. In addition, it is shown that the GPR model in the nonlinear channel equalization process can be understood as an optimized single-layer neural network model with infinite width.